Average Error: 0.0 → 0.0
Time: 2.7s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
double f(double x) {
        double r9244 = 2.0;
        double r9245 = 1.0;
        double r9246 = x;
        double r9247 = r9245 - r9246;
        double r9248 = r9245 + r9246;
        double r9249 = r9247 / r9248;
        double r9250 = sqrt(r9249);
        double r9251 = atan(r9250);
        double r9252 = r9244 * r9251;
        return r9252;
}
↓
double f(double x) {
        double r9253 = 2.0;
        double r9254 = 1.0;
        double r9255 = x;
        double r9256 = r9254 - r9255;
        double r9257 = r9254 + r9255;
        double r9258 = r9256 / r9257;
        double r9259 = sqrt(r9258);
        double r9260 = atan(r9259);
        double r9261 = r9253 * r9260;
        return r9261;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]

  2. Final simplification0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))